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On link maps and their homotopy classification

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References

  1. Atinah, M., Bott, R., Shapiro, A.: Clifford modules. Topology3 [Suppl. 1], 3–38 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  2. Adams, J.F.: Vector fields on spheres. Ann. Math.75, 603–632 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  3. Adams, J.F.: On the non-existence of elements of Hopf invariant one. Ann. Math.72, 20–104 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dax, J.P.: Etude homotopique des espaces de plongements. Ann. Sci. Ec. Norm. Super. Ser.6, 303–377 (1972)

    MathSciNet  MATH  Google Scholar 

  5. Fenn, R., Rolfsen, D.: Spheres may link homotopically in 4-space. J. Lond. Math. Soc.34, 177–184 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hirsch, M.: Immersions of manifolds. Trans. Am. Math. Soc.93, 242–276 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  7. James, I.: On the iterated suspension. Quart. J. Math. Oxf.5, 1–10 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kirk, P.: Link maps in the 4-sphere. Proc. Siegen Topology Symp., (Lecture Notes Mathematics, Vol. 1350) Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  9. Kirk, P.: Link homotopy with one codimension 2 component. Trans. Am. Math. Soc., to appear

  10. Kirk, P.: Embedded links with one codimension 2 component are nullhomotopic in the metastable range. Brandeis University, preprint (1988)

  11. Koschorke, U.: Vector fields and other vector bundle morphisms — a singularity approach. (Lecture Notes Mathematics, Vol. 847). Berlin Heidelberg New York: Springer 1981

    Book  MATH  Google Scholar 

  12. Koschorke, U.: Higher order homotopy invariants for higher dimensional link maps. (Lecture Notes Mathematics, Vol. 1172, pp. 116–129). Berlin Heidelberg New York: Springer 1985

    MATH  Google Scholar 

  13. Koschorke, U.: Link maps and the geometry of their invariants. Manuscr. Math.61, 383–415 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Koschorke, U.: Desuspending the α-invariant of link maps, Proceedings of the Baku Topology Conference (1987), to appear in Lecture Notes Mathematics, Springer

  15. Koschorke, U.: Multiple point invariants of link maps. Proc. Second Siegen Topology Symposium 1987. (Lecture Notes Mathematics, Vol. 1350, pp. 44–86). Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  16. Koschorke, U.: Link maps with many components. Topology (to appear)

  17. Koschorke, U., Sanderson, B.: Geometric interpretations of the generalized Hopf invariant. Math. Scand.41, 199–217 (1977)

    MathSciNet  MATH  Google Scholar 

  18. Milnor, J.: Link groups. Ann. Math.59, 177–195 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  19. Massey, W., Rolfsen, D.: Homotopy classification of higher dimensional links. Indiana Univ. Math. J.34, 375–391 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  20. Paechter, G.F.: The groups π R (V n, m )(I). Quart. J. Math. Oxf.7, 249–268 (1956)

    Article  MathSciNet  Google Scholar 

  21. Salomonsen, M.A.: Bordism and geometric dimension. Math. Scand.32, 87–111 (1973)

    MathSciNet  MATH  Google Scholar 

  22. Scott, G.P.: Homotopy links. Abh. Math. Sem. Hamb.32, 186–190 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  23. Spanier, E.: Algebraic topology. Ser. in Higher Math. XIV. New York: McGraw-Hill 1966

    MATH  Google Scholar 

  24. Toda, H.: Composition methods in homotopy groups of spheres. Annals of Math. Studies, No. 49. Princeton: Princeton Univ. Press 1962

    MATH  Google Scholar 

  25. Whitehead, G.W.: On the Freudenthal theorems. Ann. Math.57, 209–228 (1953)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Fachbereich 6, Mathematik, Universität Gesamthochschule Siegen, D-5900, Siegen 21, Federal Republic of Germany

    Ulrich Koschorke

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  1. Ulrich Koschorke
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Koschorke, U. On link maps and their homotopy classification. Math. Ann. 286, 753–782 (1990). https://doi.org/10.1007/BF01453601

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